On algebraic spaces with an action of G_m

Abstract

Let Z be an algebraic space of finite type over a field, equipped with an action of the multiplicative group $G_m$. In this situation we define and study a certain algebraic space equipped with an unramified morphism to $A^1\times Z\times Z$, where $A^1$ is the affine line. (If Z is affine and smooth this is just the closure of the graph of the action map $G_m\times Z\to Z$.) In articles joint with D.Gaitsgory we use this set-up to prove a new result in the geometric theory of automorphic forms and to give a new proof of a very important theorem of T. Braden.

Appendix C added

References in corpus (3)

• Higher Topos Theory
• Derived Algebraic Geometry III: Commutative Algebra
• On a theorem of Braden

Cited by in corpus (11)

• A Luna étale slice theorem for algebraic stacks
• Existence of moduli spaces for algebraic stacks
• Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
• On a theorem of Braden
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• Kernels from Compactifications
• Resolutions with conical slices and descent for the Brauer group classes of certain central reductions of differential operators in characteristic $p$
• Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor
• Computable Białynicki-Birula decomposition of the Hilbert scheme
• Deligne--Lusztig duality on the moduli stack of bundles
• Windows for cdgas